Isn’t the issue that most dechlorinator’s take away oxygen in the water?
What a lot of hobbyists don't realise is that the dosing instructions on dechlorinator are to neutralise 'X' amount of chlorine, but your actual chlorine levels might be different to their 'X'. I think PRIME states that 10ml of their product removes 5mg of chlorine in 100 gallons of water. This is a bit of a blanket statement by Seachem, and is great if you do indeed have 5mg of chlorine in your tap water.
If you physically check your local water report on line, very easy to do this, and find out exactly what your level of chlorine is, you can find out exactly how much dechlorinator you need.
As an example, I was dosing as per their instructions for 5mg of chlorine, but on further investigation I only have 0.75mg of chlorine in my tap water! So I was dosing FIVE times more than I needed!!! I never experienced any adverse reactions from my fish whilst dosing way more than I needed, which proves that slight overdosing isn't an issue, in fact Seachem state that you can up the dose in certain circumstances.
That said, dechlorinator is a reducing agent, and if there is very little chlorine for it to react with, as in my case, and you really overdosed on a monumental scale, then you could have problems because it would then react with the oxygen instead, like you alluded to, and you may see your fish gasping for air.
When I first started using SAFE i got the measurements wrong and my fish were really stressed. SAFE is a lot easier to overdose because the levels needed are tiny, especially in small tanks.